Activities of P₂O₅ in Solid Solutions between Di-calcium Silicate and Tri-calcium Phosphate at 1573 K

Abstract

The knowledge of P₂O₅ activities in solid solutions between Ca₂SiO₄ and Ca₃P₂O₈ is required for more effective dephosphorization. In the present study, firstly, the P₂O₅ activities in these solid solutions coexisting with CaO or CaSiO₃ at 1573 K were measured by equilibrating molten copper with oxide phases under a stream of Ar + H₂ + H₂O gas mixtures. Subsequently, the sub-regular solution model was applied to Ca₂SiO₄–Ca₃P₂O₈ solid solutions. The P₂O₅ activities calculated with the solution model agreed well with the present experimental results and the literature data. It was found that the P₂O₅ activity in Ca₂SiO₄–Ca₃P₂O₈ solid solution coexisting with CaO was about 7 digits lower than that coexisting with CaSiO₃.

1. Introduction

The dephosphorization reaction in steelmaking processes can be formulated by   

$$2{[\mathrm{P}]}_{\mathrm{F}\mathrm{e}}+5{(\mathrm{F}\mathrm{e}\mathrm{O})}_{\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{g}}={({\mathrm{P}}_2{\mathrm{O}}_5)}_{\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{g}}+5\left\{\mathrm{F}\mathrm{e}\right\}$$(1)

, where [P]_Fe is phosphorus in liquid iron, (FeO)_slag and (P₂O₅)_slag represent FeO and P₂O₅ in slag, respectively, and {Fe} indicates liquid iron. According to Le Chatelier’s principle, the thermochemical conditions for effective dephosphorization are low P₂O₅ activity, high FeO activity, and low temperature. In order to decrease P₂O₅ activities in slags, CaO is added, and then P₂O₅ often is present in solid solutions between di-calcium silicate, Ca₂SiO₄, and tri-calcium phosphate, Ca₃P₂O₈,¹⁾ as seen in Fig. 1(a); the pseudo-binary phase diagram of Ca₂SiO₄ and Ca₃P₂O₅ reported by Fix et al.²⁾ Hereafter, the following abbreviations are used.   

$$\begin{array}{l}{C}_{3}S=\mathrm{C}{\mathrm{a}}_3\mathrm{S}\mathrm{i}{\mathrm{O}}_5=3\mathrm{C}\mathrm{a}\mathrm{O}\cdot \mathrm{S}\mathrm{i}{\mathrm{O}}_2\\ C_{2}S=\mathrm{C}{\mathrm{a}}_2\mathrm{S}\mathrm{i}{\mathrm{O}}_4=2\mathrm{C}\mathrm{a}\mathrm{O}\cdot \mathrm{S}\mathrm{i}{\mathrm{O}}_2\\ C_3{S}_2=\mathrm{C}{\mathrm{a}}_3\mathrm{S}{\mathrm{i}}_2{\mathrm{O}}_7=3\mathrm{C}\mathrm{a}\mathrm{O}\cdot 2\mathrm{S}\mathrm{i}{\mathrm{O}}_2\\ CS=\mathrm{C}\mathrm{a}\mathrm{S}\mathrm{i}{\mathrm{O}}_3=\mathrm{C}\mathrm{a}\mathrm{O}\cdot \mathrm{S}\mathrm{i}{\mathrm{O}}_2\\ C_{4}P=\mathrm{C}{\mathrm{a}}_4{\mathrm{P}}_2{\mathrm{O}}_9=4\mathrm{C}\mathrm{a}\mathrm{O}\cdot {\mathrm{P}}_2{\mathrm{O}}_5\\ C_{3}P=\mathrm{C}{\mathrm{a}}_3{\mathrm{P}}_2{\mathrm{O}}_8=3\mathrm{C}\mathrm{a}\mathrm{O}\cdot {\mathrm{P}}_2{\mathrm{O}}_5\\ <C_{2}S-C_{3}P>ss=\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{i}\mathrm{d}\mathrm{\hspace{0.17em} } \mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{\hspace{0.17em} } \mathrm{b}\mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n}\mathrm{\hspace{0.17em} } \mathrm{C}{\mathrm{a}}_2\mathrm{S}\mathrm{i}{\mathrm{O}}_4\mathrm{\hspace{0.17em} } \mathrm{a}\mathrm{n}\mathrm{d}\mathrm{\hspace{0.17em} } \mathrm{C}{\mathrm{a}}_3{\mathrm{P}}_2{\mathrm{O}}_8\\ C_{7}P{S}_2=\mathrm{C}{\mathrm{a}}_7{\mathrm{P}}_2\mathrm{S}{\mathrm{i}}_2{\mathrm{O}}_{16}=7\mathrm{C}\mathrm{a}\mathrm{O}\cdot {\mathrm{P}}_2{\mathrm{O}}_5\cdot 2\mathrm{S}\mathrm{i}{\mathrm{O}}_2\\ C_{5}PS=\mathrm{C}{\mathrm{a}}_5{\mathrm{P}}_2\mathrm{S}\mathrm{i}{\mathrm{O}}_{12}=5\mathrm{C}\mathrm{a}\mathrm{O}\cdot {\mathrm{P}}_2{\mathrm{O}}_5\cdot \mathrm{S}\mathrm{i}{\mathrm{O}}_2\end{array}$$

Based on this consideration, a number of investigations have been conducted to determine activities of P₂O₅ in dephosphorization slags.

Fig. 1.

(a) Phase diagram of the Ca₂SiO₄–Ca₃P₂O₈ pseudo-binary system,²⁾ (b) Iso-thermal section of the CaO–SiO₂–P₂O₅ ternary system at 1573 K.³⁾

Figure 1(b) gives the phase relationship in the region of CaO–CaSiO₃–Ca₃P₂O₈ of the ternary system CaO–SiO₂–P₂O₅ at 1573 K.³⁾ The thermochemical data on the formations of C₄P and C₃P from CaO and P₂O₅ have been reported as   

$$4\mathrm{\hspace{0.17em} }\mathrm{C}\mathrm{a}\mathrm{O}+{\mathrm{P}}_2{\mathrm{O}}_5=C_{\mathit{4}}P$$(2)

  

$$\begin{array}{l}\text{log}\mathrm{\hspace{0.17em} }K(2)=\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{4}P}-4\mathrm{\hspace{0.17em} }\text{log}\mathrm{\hspace{0.17em} }{a}_{CaO}-\text{log}\mathrm{\hspace{0.17em} }{a}_{P_2{O}_5}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=25.18\hspace{1em}\hspace{1em}\mathrm{a}\mathrm{t}\mathrm{\hspace{0.17em} } 1\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} } \mathrm{K}\end{array}$$(3) ^4,5)

  

$$3\mathrm{\hspace{0.17em} }\mathrm{C}\mathrm{a}\mathrm{O}+{\mathrm{P}}_2{\mathrm{O}}_5=C_{\mathit{3}}P$$(4)

  

$$\begin{array}{l}\text{log}\mathrm{\hspace{0.17em} }K(4)=\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{3}P}-3\mathrm{\hspace{0.17em} }\text{log}\mathrm{\hspace{0.17em} }{a}_{CaO}-\text{log}\mathrm{\hspace{0.17em} }{a}_{P_2{O}_5}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=24.80\hspace{1em}\hspace{1em} \mathrm{a}\mathrm{t}\mathrm{\hspace{0.17em} } 1\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} } \mathrm{K}\end{array}$$(5) ^4,5,6)

By using Eqs. (3) and (5), the P₂O₅ activities, a_P2O5, in the three-phase region of CaO + C₅PS + C₄P and the two-phase assemblage of C₄P + C₃P could be derived as follows, respectively.   

$$\begin{array}{l}\mathrm{r}\mathrm{e}\mathrm{g}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{\hspace{0.17em} } \mathrm{o}\mathrm{f}\mathrm{\hspace{0.17em} } \mathrm{C}\mathrm{a}\mathrm{O}+C_{\mathit{5}}PS+C_{\mathit{4}}P\\ \text{log}\mathrm{\hspace{0.17em} }{a}_{P_2{O}_5}=-\text{log}\mathrm{\hspace{0.17em} }K(2)=-25.18\hspace{1em}\mathrm{a}\mathrm{t}\mathrm{\hspace{0.17em} } 1\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} } \mathrm{K}\end{array}$$(6)

  

$$\begin{array}{l}\mathrm{r}\mathrm{e}\mathrm{g}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{\hspace{0.17em} } \mathrm{o}\mathrm{f}\mathrm{\hspace{0.17em} } C_{\mathit{4}}P+C_{\mathit{3}}P\\ \text{log}\mathrm{\hspace{0.17em} }{a}_{P_2{O}_5}=3log\mathrm{\hspace{0.17em} }K(2)-4\mathrm{\hspace{0.17em} }\text{log}\mathrm{\hspace{0.17em} }K(4)=-23.66\hspace{1em}\mathrm{a}\mathrm{t}\mathrm{\hspace{0.17em} } 1\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} } \mathrm{K}\end{array}$$(7)

Takeshita et al. measured a_P2O5 in the three-phase region of C₃S + C₂S + <C₂S–C₃P>ss through a gas equilibrium method, in which molten copper containing phosphorus was coexisted with oxides under a stream of Ar + H₂ + H₂O gas mixtures.⁷⁾ The result was given as   

$$\begin{array}{l}\mathrm{r}\mathrm{e}\mathrm{g}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{\hspace{0.17em} }\hspace{0.17em}\mathrm{o}\mathrm{f}\mathrm{\hspace{0.17em} } C_{\mathit{3}}S+C_{\mathit{2}}S+<C_{\mathit{2}}S-C_{\mathit{3}}P>ss\\ \text{log}\mathrm{\hspace{0.17em} }{a}_{P_2{O}_5}=-26.53\hspace{1em}\mathrm{a}\mathrm{t}\mathrm{\hspace{0.17em} } 1\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} } \mathrm{K}\end{array}$$(8)

At higher temperatures than 1573 K, Zhong et al. measured the P₂O₅ activities in <C₂S–C₃P>ss at 1823 K and 1873 K by equilibrating phosphorus-containing iron with solid solutions in oxygen partial pressures controlled by CO + CO₂ gas mixtures.^8,9,10)

Figure 2 is a schematic diagram of the phase relationship in the CaO–SiO₂–P₂O₅–FeO quaternary system at 1573 K. The base CaO–SiO₂–P₂O₅ of this tetrahedron represents the phase diagram of the corresponding ternary system at 1573 K. It has been reported by Uchida et al. that there was the three-phase region of SiO₂ + CS + C₃P.^11,12) By combining Eq. (5) and the thermochemical data on the formation of CS given in Eq. (10), the P₂O₅ activity could be derived as follows.   

$$\mathrm{C}\mathrm{a}\mathrm{O}+\mathrm{S}\mathrm{i}{\mathrm{O}}_2=CS$$(9)

  

$$\begin{array}{l}\text{log}\mathrm{\hspace{0.17em} }K(9)=\text{log}\mathrm{\hspace{0.17em} }{a}_{CS}-\text{log}\mathrm{\hspace{0.17em} }{a}_{CaO}-\text{log}\mathrm{\hspace{0.17em} }{a}_{Si{O}_2}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=2.92\hspace{1em}\hspace{1em}\mathrm{a}\mathrm{t}\mathrm{\hspace{0.17em} } 1\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} } \mathrm{K}\end{array}$$(10) ^13,14)

  

$$\begin{array}{l}\mathrm{r}\mathrm{e}\mathrm{g}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{\hspace{0.17em} } \mathrm{o}\mathrm{f}\mathrm{\hspace{0.17em} } \mathrm{S}\mathrm{i}{\mathrm{O}}_2+CS+C_{\mathit{3}}P\\ \begin{array}{l}\text{log}\mathrm{\hspace{0.17em} }{a}_{P_2{O}_5}=log\mathrm{\hspace{0.17em} }{a}_{C_{3}P}-3log\mathrm{\hspace{0.17em} }{a}_{CaO}-log\mathrm{\hspace{0.17em} }K(4)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=-3[-\text{log}\mathrm{\hspace{0.17em} }K(9)]-log\mathrm{\hspace{0.17em} }K(4)=-16.04\hspace{1em}\mathrm{a}\mathrm{t}\mathrm{\hspace{0.17em} } 1\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} } \mathrm{K}\end{array}\end{array}$$(11)

When iron oxide was added to the CaO–SiO₂–P₂O₅ ternary slags, <C₂S–C₃P>ss could coexist with quaternary liquid phase, hereafter represented as “Liquid”. Matsugi et al. determined simultaneously the activities of P₂O₅ and FeO in the three-phase region of CS + <C₂S–C₃P>ss + Liquid at 1573 K by employing electrochemical technique incorporating MgO-stabilized zirconia.¹⁵⁾ Pahlevani et al. calculated the P₂O₅ activities in the two-phase region of <C₂S–C₃P>ss + Liquid at 1573 K by applying the regular solution model to Liquid.¹⁶⁾ For better understanding of dephosphorization reaction, the knowledge of P₂O₅ activities in <C₂S–C₃P>ss would be necessary, whereas there has been still lack of data measured at temperature of hot metal processing. In this study, firstly, the activities of P₂O₅ were measured in <C₂S–C₃P>ss at 1573 K to investigate the effects of coexisting solid phases, i.e., CaO or CS, on the P₂O₅ activities. Subsequently, the parameters in the sub-regular solution model applied to <C₂S–C₃P>ss were optimized by using the experimental data to discuss the thermochemical properties in the CaO–SiO₂–P₂O₅ ternary system.

Fig. 2.

Schematic diagram of phase relationship in the CaO–SiO₂–P₂O₅–FeO quaternary system at 1573 K.

2. Experimental Aspects

2.1. Principle of Measurements

In order to determine the P₂O₅ activities in the heterogeneous slags, molten copper was brought into equilibrium with oxide mixtures under a stream of Ar + H₂ + H₂O gas mixtures. The reaction underlying the present study can be formulated as   

$$2\mathrm{\hspace{0.17em} }{\text{[}\mathrm{P}\text{]}}_{\mathrm{C}\mathrm{u}}+5\mathrm{\hspace{0.17em} }{\mathrm{H}}_2\mathrm{O}(\mathrm{g}\mathrm{a}\mathrm{s})={({\mathrm{P}}_2{\mathrm{O}}_5)}_{\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{g}}+5\mathrm{\hspace{0.17em} }{\mathrm{H}}_2(\mathrm{g}\mathrm{a}\mathrm{s})$$(12)

, where [P]_Cu and (P₂O₅)_slag denote phosphorus in liquid copper and P₂O₅ in slag, respectively. The Gibbs energy change for the dissolution of gaseous phosphorus into liquid copper at 1 mass% solution was reported as   

$$(1/2)\mathrm{\hspace{0.17em} }{\mathrm{P}}_2(\mathrm{g}\mathrm{a}\mathrm{s})={[\mathrm{P}]}_{\mathrm{C}\mathrm{u}}$$(13)

  

$$\mathrm{\Delta }G°(13)/\text{J}\cdot {\text{mol}}^{-1}=-125\mathrm{\hspace{0.17em} }000+0.54(T/\text{K})$$(14) ¹⁷⁾

The standard Gibbs energy changes for the following reactions were also available in the literature.   

$${\mathrm{P}}_2(\mathrm{g}\mathrm{a}\mathrm{s})+(5/2)\mathrm{\hspace{0.17em} }{\mathrm{O}}_2(\mathrm{g}\mathrm{a}\mathrm{s})={\mathrm{P}}_2{\mathrm{O}}_5(\mathrm{l}\mathrm{i}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{d})$$(15)

  

$$\mathrm{\Delta }G°(15)/\text{J}\cdot {\text{mol}}^{-1}=-1\mathrm{\hspace{0.17em} }534\mathrm{\hspace{0.17em} }500+506.3(T/\text{K})$$(16) ⁴⁾

  

$${\mathrm{H}}_2(\mathrm{g}\mathrm{a}\mathrm{s})+(1/2){\mathrm{O}}_2(\mathrm{g}\mathrm{a}\mathrm{s})={\mathrm{H}}_2\mathrm{O}(\mathrm{g}\mathrm{a}\mathrm{s})$$(17)

  

$$\mathrm{\Delta }G°(17)/\text{J}\cdot {\text{mol}}^{-1}=-246\mathrm{\hspace{0.17em} }000+54.8(T/\text{K})$$(18) ¹⁸⁾

Hence, by combining Eqs. (14), (16) and (18), the equilibrium constant for reaction (12) at 1573 K is given by   

$$\begin{array}{l}\text{log}\mathrm{\hspace{0.17em} }K(12)=5\mathrm{\hspace{0.17em} }\text{log(}{P}_{H_2}/P_{H_{2}O}\text{)}+\text{log}\mathrm{\hspace{0.17em} }{a}_{P_2{O}_5}-2\mathrm{\hspace{0.17em} }\text{log}\mathrm{\hspace{0.17em} }{h}_P\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=-10.34\hspace{1em}\hspace{1em}\mathrm{a}\mathrm{t}\mathrm{\hspace{0.17em} } 1\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} } \mathrm{K}\end{array}$$(19)

In Eq. (19), the standard state of the P₂O₅ activity is taken to be pure hypothetical liquid P₂O₅. At low phosphorus concentrations, the Henrian activity of phosphorus in liquid copper, h_P, would be equal to the phosphorus concentration in mass percent, [mass%P]_Cu, Therefore, Eq. (19) can be rewritten by   

$$\begin{array}{l}\text{log}\mathrm{\hspace{0.17em} }{a}_{P_2{O}_5}=-5\mathrm{\hspace{0.17em} }\text{log(}{P}_{H_2}/P_{H_{2}O}\text{)}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+2\mathrm{\hspace{0.17em} }\text{log[}mass\%P{\text{]}}_{Cu}-10.34\hspace{1em}\hspace{1em}\mathrm{a}\mathrm{t}\mathrm{\hspace{0.17em} } 1\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} } \mathrm{K}\end{array}$$(20)

Equation (20) indicates that the values for a_P2O5 at 1573 K can be determined by analyzing [mass%P]_Cu in liquid copper equilibrated with the heterogeneous slags under a stream of Ar + H₂ + H₂O gas mixtures in which P_H2/P_H2O ratios are fixed.

2.2. Experimental Apparatus and Procedure

The preparation of CaO is based upon heating CaCO₃ at 1273 K for 12 hours. C₃P and SiO₂ were obtained from Nacalai Tesque, Inc., Kyoto, Japan, and dried at 413 K. C₂S and CS were obtained by mixing requisite portions of CaCO₃ and SiO₂, and then heating at 1573 K for 24 hours and 98 hours, respectively. The solid solutions, <C₂S–C₃P>ss, were prepared by mixing C₂S and C₃P, and heating at 1573 K for 24 hours. The starting materials thus obtained were mixed to yield the bulk compositions listed in Table 1. In this table and hereafter, (mass%C₃P)_SS represents the C₃P concentration in <C₂S–C₃P>ss. The oxide mixtures used in this study occurred at the two-phase regions of CaO + <C₂S–C₃P>ss and CS + <C₂S–C₃P>ss, illustrated in Fig. 1(b).

Table 1. Experimental conditions and results at 1573 K.

Region	Bulk composition (mass%)			(mass%C3P)ss	PH2 (atm)	PH2O (atm)	[mass%P]Cu	log aP2O5
	CaO	SiO2	P2O5
CaO + <C2S–C3P>ss	68.75	19.64	11.60	31	1.20×10−1	2.23×10−4	0.064 ±0.004	−26.43 ±0.05
CS + <C2S–C3P>ss	55.72	40.16	4.12	18	1.20×10−1	8.53×10−3	0.015 ±0.002	−19.73 ±0.10
	55.39	39.12	5.49	24	1.20×10−1	8.53×10−3	0.017 ±0.002	−19.62 ±0.09
	550.1	37.90	7.09	31	1.20×10−1	8.53×10−3	0.021 ±0.004	−19.44 ±0.15

The experimental apparatus and associated gas trains, respectively, are schematically shown in Figs. 3 and 4. A SiC resistance furnace was equipped with a mullite reaction tube of 60-mm o.d., 50-mm i.d. and 1000-mm in length. About 1-g of pure copper and about 0.6-g of the oxide mixtures were charged in alumina crucibles of 10-mm o.d., 8-mm i.d. and 30-mm in height. Seven crucibles were put into a nickel container of 38-mm o.d., 32-mm i.d. and 63-mm in height. This container was suspended from the furnace top via a nickel rod of 3-mm diameter and heated up to 1573 K. Within the crucibles, copper was placed between the oxide mixtures, as shown in Fig. 3. The oxide mixtures, initially placed beneath the copper, did not rise up to the top of the molten copper surface. This arrangement was conducted to increase the contact area between oxide and copper. The oxide mixture on liquid copper was powdery and its thickness was about 2-mm; it would not prevent the contact between liquid copper and gas phase. In the experimental runs, the gas mixtures of Ar + H₂ + H₂O were introduced into the reaction tube at a flow rate of 200 mL/min.

Fig. 3.

Experimental apparatus. (A) Gas inlet, (B) Water-cooled brass flange, (C) Rubber stopper, (D) Nickel rod, (E) Mullite reaction tube, (F) Pt-PtRh13 thermocouple, (G) Alumina sheath, (H) Nickel container, (I) Alumina crucible, (J) Oxide mixture, (K) {Cu–P} liquid alloy, (L) Water-cooled brass flange, (M) Gas outlet.

Fig. 4.

Gas trains. (A) Ar + H₂ gas cylinder, (B) Silica-gel, (C) Phosphorus pentoxide, (D) Cold trap, (E) Thermostat bath, (F) C₂H₂O₄·2H₂O + C₂H₂O₄ mixture, (G) LiCl·2H₂O-saturated water, (H) Two-way stopcock, (I) Furnace assembly, (J) Empty tube, (K) Di-n-butyl-phthalate bleeder.

Temperatures were measured with a Pt-PtRh13 thermocouple placed beside the nickel container, and controlled to ±1 K by using a control thermocouple and a PID-type temperature regulator. The overall errors in temperature measurements and control were estimated to be less than ±2 K.

The two-phase oxide of CaO + <C₂S–C₃P>ss was brought into equilibrium with Cu–P alloys under a stream of the Ar + H₂ + H₂O gas mixture prepared by passing Ar + 12%H₂ gas mixture through C₂H₂O₄·2H₂O + C₂H₂O₄ mixture kept at 268 K within a thermostat bath. The equilibrium partial pressure of H₂O fixed by this two-phase mixture has been reported elsewhere;¹⁹⁾   

$$\text{log(}{P}_{H_{2}O}/\text{atm)}=6.88-2\mathrm{\hspace{0.17em} }810/(T/\text{K})\hspace{1em}\mathrm{\hspace{0.17em} }T<293\mathrm{\hspace{0.17em} } \text{K}$$(21)

The water vapor pressures used in this study were much lower than those obtainable through the conventional technique. Thus, the Ar + H₂ gas mixture has to be rigidly moisture-free; the gas trains for Ar + H₂ gas mixture contained silica gel, phosphorus pentoxide and a cold trap kept below 223 K, as illustrated in Fig. 4.

On the other hand, in the case of the two-phase oxide mixtures of CS + <C₂S–C₃P>ss, the Ar + H₂ + H₂O gas mixture was prepared by passing Ar + 12%H₂ gas mixture through LiCl·2H₂O-saturated water kept at 313 K. The equilibrium H₂O partial pressure of LiCl·2H₂O-saturated water has been also reported elsewhere;¹⁹⁾   

$$\text{log(}{P}_{H_{2}O}/\text{atm)}=5.94-2\mathrm{\hspace{0.17em} }510/(T/\text{K})\hspace{1em}\mathrm{\hspace{0.17em} }T>291.5\mathrm{\hspace{0.17em} } \text{K}$$(22)

The experimental conditions are summarized in Table 1.

After the furnace was kept at the experimental temperature for 22 hours, the nickel container was lowered onto the bottom of the water-cooled brass flange inside the furnace tube. The oxide mixtures were then removed from the alumina crucibles, ground and subsequently charged again into the crucibles for repeated durations. These procedures were repeated at an interval of 22 hours. In this study, these procedures were essential, because neither metal nor oxide phases could be agitated during experimental runs. Any unexpected reactions could not be observed between the oxide mixtures and alumina crucibles.

For analyzing phosphorus contents in copper, samples were dissolved in HCl + HNO₃ solution. In order to separate copper and phosphorus, ammonium phosphor-molybdate was precipitated from the solution by addition of ammonium molybdate. After being filtered, the precipitate was dissolved in NaOH solution, and subsequently phosphorus was analyzed with an inductive-coupled plasma spectrometer.

3. Experimental Results and Discussion

3.1. Activity Measurements

Figure 5 gives a typical relation between phosphorus content in liquid copper coexisting with oxide mixture of CS + <C₂S–C₃P>ss of (mass%C₃P)_SS = 31 and duration at 1573 K. Although there were experimental variations, the equilibrium value for [mass%P]_Cu could be obtained if the experiment was continued for 120 hours and more. Taking the mass balance of phosphorus between oxide and metallic phases into account, the change of C₃P concentration in <C₂S–C₃P>ss could be estimated to be less than 0.3-mass%.

Fig. 5.

Typical relation between phosphorus content in liquid copper and duration at 1573 K.

The experimental results are summarized in Table 1, and Fig. 6 shows the P₂O₅ activities at 1573 K plotted against (mass%C₃P)_SS. The P₂O₅ activity in the two-phase region of CS + <C₂S–C₃P>ss increased with an increase in (mass%C₃P)_SS. In this two-phase region, the reactions expressed by Eqs. (4), (9) and (23) achieved the equilibrium states.   

$$2\mathrm{\hspace{0.17em} }\mathrm{C}\mathrm{a}\mathrm{O}+\mathrm{S}\mathrm{i}{\mathrm{O}}_2=C_{\mathit{2}}S$$(23)

  

$$\begin{array}{l}\text{log}\mathrm{\hspace{0.17em} }K(23)=\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{2}S}-2\mathrm{\hspace{0.17em} }\text{log}\mathrm{\hspace{0.17em} }{a}_{CaO}-\text{log}\mathrm{\hspace{0.17em} }{a}_{Si{O}_2}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=4.78\hspace{1em}\hspace{1em}\mathrm{a}\mathrm{t}\mathrm{\hspace{0.17em} } 1\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} } \mathrm{K}\end{array}$$(24) ^13,14)

By combining Eqs. (5), (10) and (24), we obtained   

$$\text{log}\mathrm{\hspace{0.17em} }{a}_{P_2{O}_5}=\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{3}P}-3\mathrm{\hspace{0.17em} }\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{2}S}-19.22\hspace{1em}\mathrm{\hspace{0.17em} }\mathrm{a}\mathrm{t}\mathrm{\hspace{0.17em} } 1\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} } \mathrm{K}$$(25)

Equation (25) indicated that the P₂O₅ activity in <C₂S–C₃P>ss coexisting with CS increased as (mass%C₃P)_SS increased at a constant temperature, due to an increase in the C₃P activity and a decrease in the C₂S activity. Therefore, the relationship between a_P2O5 and (mass%C₃P)_SS illustrated in Fig. 6 was thermodynamically consistent with Eq. (25).

Fig. 6.

Relation between logarithmic value for P₂O₅ activity and C₃P content in <C₂S–C₃P>ss at 1573 K.

Figure 6 also shows that a_P2O5 in the two-phase region of CaO + <C₂S–C₃P>ss is about 7 digits lower than that in the two-phase region of CS + <C₂S–C₃P>ss at the same C₃P content in <C₂S–C₃P>ss. The thermodynamic consistency of this behavior was discussed based on the comparisons of the CaO and SiO₂ activities in the CaO–SiO₂–P₂O₅ ternary system derived by using the present experimental results with those in the CaO–SiO₂ binary system, described as follows.

The P₂O₅ activities measured in this study are given in cells (b) and (h) of Table 2. Considering the experimental conditions, the activities of CaO and CS are unity in cells (a) and (j), respectively. Therefore, by inserting the activities of CaO and P₂O₅ into Eq. (5), we can obtain   

$$\begin{array}{l}\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{3}P}(\text{cell}\mathrm{\hspace{0.17em} }e)=\text{log}\mathrm{\hspace{0.17em} }K(4)+3\mathrm{\hspace{0.17em} }\text{log}\mathrm{\hspace{0.17em} }{a}_{CaO}(\text{cell}\mathrm{\hspace{0.17em} }a)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+\text{log}\mathrm{\hspace{0.17em} }{a}_{P_2{O}_5}(\text{cell}\mathrm{\hspace{0.17em} }b)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.5em}=24.80+3\times 0+(-26.43)=-1.63\end{array}$$(26)

Now, it can be assumed that the C₃P activity remains constant in <C₂S–C₃P>ss of (mass%C₃P)_SS = 31, whether <C₂S–C₃P>ss coexists with CaO or CS.   

$$\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{3}P}(\text{cell}\mathrm{\hspace{0.17em} }k)=\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{3}P}(\text{cell}\mathrm{\hspace{0.17em} }e)=-1.63$$(27)

Then, the followings are obtainable from Eqs. (5), (10), (24) and (27).   

$$\begin{array}{l}\text{log}\mathrm{\hspace{0.17em} }{a}_{CaO}(\text{cell}\mathrm{\hspace{0.17em} }g)\\ =[\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{3}P}(\text{cell}\mathrm{\hspace{0.17em} }k)-\text{log}\mathrm{\hspace{0.17em} }K(4)-\text{log}\mathrm{\hspace{0.17em} }{a}_{P_2{O}_5}(\text{cell}\mathrm{\hspace{0.17em} }h)]/3\\ =[(-1.63)-24.80-(-19.44)]/3=-2.33\end{array}$$(28)

  

$$\begin{array}{l}\text{log}\mathrm{\hspace{0.17em} }{a}_{Si{O}_2}(\text{cell}\mathrm{\hspace{0.17em} }i)\\ =\text{log}\mathrm{\hspace{0.17em} }{a}_{CS}(\text{cell}\mathrm{\hspace{0.17em} }j)-\text{log}\mathrm{\hspace{0.17em} }{a}_{CaO}(\text{cell}\mathrm{\hspace{0.17em} }g)-\text{log}\mathrm{\hspace{0.17em} }K(9)\\ =0-(-2.33)-2.92=-0.59\end{array}$$(29)

  

$$\begin{array}{l}\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{2}S}(\text{cell}\mathrm{\hspace{0.17em} }l)\\ =2\mathrm{\hspace{0.17em} }\text{log}\mathrm{\hspace{0.17em} }{a}_{CaO}(\text{cell}\mathrm{\hspace{0.17em} }g)+\text{log}\mathrm{\hspace{0.17em} }{a}_{Si{O}_2}(\text{cell}\mathrm{\hspace{0.17em} }i)+\text{log}\mathrm{\hspace{0.17em} }K(23)\\ =2\times (-2.33)+(-0.59)+4.78=-0.47\end{array}$$(30)

It can be assumed again that the C₂S activity is constant in <C₂S–C₃P>ss of (mass%C₃P)_SS = 31.   

$$\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{2}S}(\text{cell}\mathrm{\hspace{0.17em} }f)=\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{2}S}(\text{cell}\mathrm{\hspace{0.17em} }l)=-0.47$$(31)

By using Eqs. (24) and (31), we have   

$$\begin{array}{l}\text{log}\mathrm{\hspace{0.17em} }{a}_{Si{O}_2}(\text{cell}\mathrm{\hspace{0.17em} }c)\\ =\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{2}S}(\text{cell}\mathrm{\hspace{0.17em} }f)-2\mathrm{\hspace{0.17em} }\text{log}\mathrm{\hspace{0.17em} }{a}_{CaO}(\text{cell}\mathrm{\hspace{0.17em} }a)-\text{log}\mathrm{\hspace{0.17em} }K(23)\\ =(-0.47)-2\times 0-4.78=-5.25\end{array}$$(32)

On the other hand, the CaO and SiO₂ activities in the CaO–SiO₂ binary system can be calculated by using the thermodynamic data,^13,14) and are illustrated in Fig. 7. As seen in this figure, the ranges of the CaO and SiO₂ activities coexisting with CS at 1573 K are as follows.   

$$-2.92\le \text{log}\mathrm{\hspace{0.17em} }{a}_{CaO}\le -2.07$$(33)

  

$$-0.85\le \text{log}\mathrm{\hspace{0.17em} }{a}_{Si{O}_2}\le 0$$(34)

Equations (28) and (29) were consistent with Eqs. (33) and (34), respectively.

Table 2. Calculation results of activities in the CaO–SiO₂–P₂O₅ ternary system at 1573 K.

Region	(mass%C3P)ss	log aCaO		log aP2O5		log aSiO2		log aCS		log aC3P		log aC2S
CaO + <C2S–C3P>ss	31	(a)	0	(b)	−26.43	(c)	−5.25	(d)	–	(e)	−1.63	(f)	−0.47
CS + <C2S–C3P>ss	31	(g)	−2.33	(h)	−19.44	(i)	−0.59	(j)	0	(k)	−1.63	(l)	−0.47

Fig. 7.

Activities of CaO and SiO₂ in the CaO–SiO₂ binary system at 1573 K.

As shown in Fig. 1(b), (mass%C₃P)_SS in the three-phase coexistence of CaO + C₃S + <C₂S–C₃P>ss is lower than 31, and the SiO₂ activity in this three-phase region is equal to that in the two-phase region of CaO + C₃S; log a_SiO2 = −4.81 at 1573 K, seen in Fig. 7, while Table 2 gives log a_SiO2 = −5.25 in <C₂S–C₃P>ss of (mass%C₃P)_SS = 31 coexisting with CaO. Considering Eq. (24), this result was consistent with the thermochemical consideration that, in the case of coexisting with CaO, the SiO₂ activity decreased as the concentration and activity of C₂S decreased in <C₂S–C₃P>ss. As already mentioned above, the CaO and SiO₂ activities in Table 2 were derived by using the P₂O₅ activities measured in this study. Therefore, it could be concluded that the present experimental data were not inconsistent with the phase relationship of the CaO–SiO₂–P₂O₅ ternary system.

3.2. Solution Model Applied to <C₂S–C₃P>ss

Figure 8(a) shows that <C₂S–C₃P>ss forms between α-C₂S and α-C₃P, and it is acceptable that electrically neutral molecules of “(1/2)Ca₃P₂O₈” replace with those of “Ca₂SiO₄” in solid solutions, as illustrated in Fig. 9. Based on this simple assumption, the present authors suggested the regular solution model applied to <C₂S–C₃P>ss.²⁰⁾ In this study, the solution model was modified by using the present experimental data.

Fig. 8.

(a) Phase diagram of the Ca₂SiO₄–Ca₃P₂O₈ pseudo-binary system, (b) Activity curves of C₂S and C₃P calculated at 1573 K, (c) Logarithmic values for P₂O₅ activities plotted against substitution ratio at 1573 K.

Fig. 9.

Schematic illustration of solid solution between Ca₂SiO₄ and Ca₃P₂O₈.

The substitution ratio of Ca₂SiO₄ for (1/2)Ca₃P₂O₈, Y, was defined as   

$$\begin{array}{l}Y=n_{(1/2)C{a}_3{P}_2{O}_8}/(n_{C{a}_{2}Si{O}_4}+n_{(1/2)C{a}_3{P}_2{O}_8})\\ \hspace{1em}=2n_{C{a}_3{P}_2{O}_8}/(n_{C{a}_{2}Si{O}_4}+2n_{C{a}_3{P}_2{O}_8})\end{array}$$(35)

, where n_i represents the number of moles of chemical species i in solid solutions. In order to calculate the C₂S and C₃P activities, the sub-regular solution model was applied to <C₂S–C₃P>ss, formulated as follows.   

$$\begin{array}{l}RT\mathrm{\hspace{0.17em} } \text{ln}\mathrm{\hspace{0.17em} }{a}_{C_{3}P}=2RT\mathrm{\hspace{0.17em} } \text{ln}\mathrm{\hspace{0.17em} } a_{(1/2)C{a}_3{P}_2{O}_8}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=\mathrm{\Delta }G{°}_t(C_{3}P)+2RTlnY+2A{(1-Y)}^3+2B{(1-Y)}^2\end{array}$$(36)

  

$$RT\mathrm{\hspace{0.17em} } \text{ln}\mathrm{\hspace{0.17em} }{a}_{C_{2}S}=\mathrm{\Delta }G{°}_t(C_{2}S)+RT\mathrm{\hspace{0.17em} }ln(1-Y)-A{Y}^3+\left(\frac{3}{2}A+B\right)Y^2$$(37)

In Eqs. (36) and (37), R is the gas constant, $\mathrm{\Delta }G{°}_t(i)$ represents the Gibbs energy change of the phase transformation of i, and the parameters A and B are independent of composition and temperature. The standard states of C₂S and C₃P are taken to be the most stable forms at 1573 K, i.e., α′-C₂S and α-C₃P, respectively. Equations (36) and (37) satisfy Gibbs-Duhem equation.

The thermal data on C₂S, heat capacity and heat of the phase transformation, were available.²¹⁾ By extrapolating the value for heat capacity of α-C₂S, $\mathrm{\Delta }G{°}_t(C_{2}S)$ could be calculated as   

$$\mathrm{\Delta }G{°}_t(C_{2}S)/\text{J}\cdot {\text{mol}}^{-1}=1\mathrm{\hspace{0.17em} }132\hspace{1em}\hspace{1em}\mathrm{a}\mathrm{t}\mathrm{\hspace{0.17em} } 1\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} } \mathrm{K}$$(38)

On the other hand, the heat of the phase transformation between α-C₃P and α-C₃P has been reported to be zero.²¹⁾   

$$\mathrm{\Delta }G{°}_t(C_{3}P)/\text{J}\cdot {\text{mol}}^{-1}=0\hspace{1em}\hspace{1em}\mathrm{a}\mathrm{t}\mathrm{\hspace{0.17em} } 1\mathrm{\hspace{0.17em} }573\mathrm{\hspace{0.17em} } \mathrm{K}$$(39)

Namely, Eqs. (36) and (37) could be rewritten as Eqs. (40) and (41), respectively.   

$$\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{3}P}=2log\mathrm{\hspace{0.17em} }Y+2a{(1-Y)}^3+2b{(1-Y)}^2$$(40)

  

$$\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{2}S}=3.76\times {10}^{-2}+log(1-Y)-a{Y}^3+\left(\frac{3}{2}a+b\right)Y^2$$(41)

  

$$a=A/(R\times 1\mathrm{\hspace{0.17em} }573\times \text{ln}10)$$(42)

  

$$b=B/(R\times 1\mathrm{\hspace{0.17em} }573\times \text{ln}10)$$(43)

By combining Eqs. (5) and (40), the P₂O₅ activity in <C₂S–C₃P>ss coexisting with CaO could be given as   

$$\begin{array}{l}\text{log}\mathrm{\hspace{0.17em} }{a}_{P_2{O}_5}=\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{3}P}-\text{log}\mathrm{\hspace{0.17em} }K(4)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=2log\mathrm{\hspace{0.17em} }Y+2a{(1-Y)}^3+2b{(1-Y)}^2-24.80\end{array}$$(44)

From Eqs. (5), (10), (24), (40) and (41), the P₂O₅ activity in <C₂S–C₃P>ss coexisting with CS could be also formulated as   

$$\begin{array}{l}\text{log}\mathrm{\hspace{0.17em} }{a}_{P_2{O}_5}\\ =\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{3}P}-3[\text{log}\mathrm{\hspace{0.17em} }K(9)-\text{log}\mathrm{\hspace{0.17em} }K(23)+\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{2}S}]-\text{log}\mathrm{\hspace{0.17em} }K(4)\\ =-19.22+[2logY+2a{(1-Y)}^3+2b{(1-Y)}^2]\\ -3\left[3.76\times {10}^{-2}+log(1-Y)-a{Y}^3+\left(\frac{3}{2}a+b\right)Y^2\right]\end{array}$$(45)

The optimization of the values for the parameters a and b was conducted by comparing the P₂O₅ activities measured with those calculated from Eqs. (44) and (45). Then, we obtained   

$$a=-4.98$$(46)

  

$$b=2.26$$(47)

Figure 8(b) shows the C₃P and C₂S activities calculated as functions of Y, deviated negatively from Raoult’s law. These behaviors corresponded to the chemical affinity between C₃P and C₂S in solid solutions.

Figure 8(c) illustrates the P₂O₅ activities at 1573 K in the two-phase regions of CaO + <C₂S–C₃P>ss, C₄P + <C₂S–C₃P>ss and CS + <C₂S–C₃P>ss calculated from Eqs. (44), (49), and (45), respectively.   

$$3C_{4}P+{\mathrm{P}}_2{\mathrm{O}}_5=4C_{3}P$$(48)

  

$$\begin{array}{l}\text{log}\mathrm{\hspace{0.17em} }{a}_{P_2{O}_5}=4\mathrm{\hspace{0.17em} }\text{log}\mathrm{\hspace{0.17em} }{a}_{C_{3}P}-4\mathrm{\hspace{0.17em} }\text{log}\mathrm{\hspace{0.17em} }K(4)+3\mathrm{\hspace{0.17em} }\text{log}\mathrm{\hspace{0.17em} }K(2)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=4\left[2logY-9.96\times {(1-Y)}^3+4.51\times {(1-Y)}^2\right]\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-23.66\end{array}$$(49)

Although the P₂O₅ activities were estimated too low in the region of Y < 0.2, the values for a_P2O5 calculated with the solution model were in good agreement with those in CaO + <C₂S–C₃P>ss and CS + <C₂S–C₃P>ss measured in the present study and those in C₄P + C₃P, CaO + C₅PS + C₄P and SiO₂ + CS + C₃P derived with the literature data^4,5,6) (With respect to detailed calculation methods, see introduction).

Figure 8(c) also shows the P₂O₅ activities in the three-phase region of CS + <C₂S–C₃P>ss + Liquid¹⁵⁾ and the two-phase coexistence of <C₂S–C₃P>ss + Liquid.¹⁶⁾ It could be concluded here that the values for a_P2O5 in CS + <C₂S–C₃P>ss + Liquid were slightly lower than those in CS + <C₂S–C₃P>ss due to dissolution of iron oxide into <C₂S–C₃P>ss (See Fig. 2). Considering the chemical affinity between CaO and P₂O₅, it would be expected that the P₂O₅ activity decreased with an increase in slag basicity. As seen in Fig. 8(c), the values for a_P2O5 in <C₂S–C₃P>ss + Liquid reported in the literature¹⁶⁾ were much higher than those in CaO + <C₂S–C₃P>ss and were almost equal to those in CS + <C₂S–C₃P>ss calculated in this study; these results were acceptable. However, the detailed effect of slag basicity on a_P2O5 in liquid phase saturated with <C₂S–C₃P>ss would be our important future subject.

4. Conclusion

For better understanding phosphorus removal from hot metal, the present study was aimed at measuring the P₂O₅ activities in solid solutions between Ca₂SiO₄ and Ca₃P₂O₈ coexisting with CaO or CaSiO₃ at 1573 K. It was clarified that the P₂O₅ activity in the two-phase region of CaO + Ca₂SiO₄–Ca₃P₂O₈ solid solution was about 7 digits lower than that in the two-phase region of CaSiO₃ + Ca₂SiO₄–Ca₃P₂O₈ solid solution. The values for the activities of components determined in this study were consistent with the phase relationship in the CaO–SiO₂–P₂O₅ ternary system. The P₂O₅ activities calculated with the solution model applied to Ca₂SiO₄–Ca₃P₂O₈ solid solution were in good agreement with the present experimental results and the literature data.

Acknowledgement

This work was supported by JSPS KAKENHI Grant Number 15K06524.

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